Simplify the following expression: $q = \dfrac{-6a^2 - 12a}{-18a^2 - 26a}$ You can assume $a \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-6a^2 - 12a = - (2\cdot3 \cdot a \cdot a) - (2\cdot2\cdot3 \cdot a)$ The denominator can be factored: $-18a^2 - 26a = - (2\cdot3\cdot3 \cdot a \cdot a) - (2\cdot13 \cdot a)$ The greatest common factor of all the terms is $2a$ Factoring out $2a$ gives us: $q = \dfrac{(2a)(-3a - 6)}{(2a)(-9a - 13)}$ Dividing both the numerator and denominator by $2a$ gives: $q = \dfrac{-3a - 6}{-9a - 13}$